Two problems in the theory of differential equations

文献摘要

The differential equation considered in terms of exterior differential forms, as 'E.Cartan did, singles out a differential ideal in the supercommutative superalgebra of differential forms, hence an affine supervariety. In view of this observation, it is evident that every differential equation has a supersymmetry (perhaps trivial). Superymmetries of which (systems of) classical differential equations are missed yet? Why criteria of formal integrability of differential equations are never used in practice?

The differential equation considered in terms of exterior differential forms, as 'E.Cartan did, singles out a differential ideal in the supercommutative superalgebra of differential forms, hence an affine supervariety. In view of this observation, it is evident that every differential equation has a supersymmetry (perhaps trivial). Superymmetries of which (systems of) classical differential equations are missed yet?
Why criteria of formal integrability of differential equations are never used in practice?